Clean up vertices/edges with no faces
The first tool that will help you cleanup your mesh is Select Loose Geometry which is available in the select menu in edit mode. This will select any vertices that are not connected to anything. Once selected you can simply delete these vertices.



The other one that can help is Select Similar. Start by de-selecting all vertices, then select one vertex that has a single connected edge and press ShiftG (also available in the select menu) and choose Amount of connecting edges. This will select all vertices that have one edge connected to them allowing you to delete these vertices. Repeat for any similar situations that you may want to cleanup.